I do not think proper orthogonal decomposition or principal component analysis will be useful for this problem. To do proper orthogonal decomposition on this data, you could reshape L into a 1024x1024 matrix, but the values of the predictor variables would vary in a wierd way across the rows and columns, and I don't think you would get useful results.
Let's consider lift (L) only. The same analysis can be applied to drag. You have computed lift for 2^20 combinations of 5 predictor variables (16 values per predictor). You are seeking a simplified model that predicts lift based on the values of the 5 variables, without using a look-up table. I would try regression models. The regression model may have a lot of terms, but it will still be small compared to 2^20. For example:
Model 1: Linear regression along each predictor (5 terms), plus all multiplicative interaction terms (5*4/2=10 terms) + intercept = 16 possible model coefficients.
Model 2: Quadratic regression along each predictor (10 terms) plus multiplicative interactions (10 terms) + intercept = 21 possible model coefficients.
Use fitlm() or stepwiselm() to find the coefficients and to identify which ones are significant.
Extract the data from your database to create an array X (size 2^20 x 5) of all combinations of predictor variables, and vector L=lift (size 2^20 x 1) for each row of X.
If you include quadratic or higher order regression terms, I recommend centering the predictor values, so the mean value for each predictor is 0.
Example script is attached. Part 1 of the script creates and populates array X and vector L. The second part of the script fits the lift data using Model 1 and using Model 2. It uses stepwiselm() to fit the model. The script takes about 2 minutes to run on my old notebook machine.
